The Pareto, Piecewise Pareto and Generalized Pareto Distribution
Density of the generalized Pareto Distribution
Density of the Pareto Distribution
Density of the Piecewise Pareto Distribution
Expected Frequency in Excess of a Threshold
Expected Frequency in Excess of a Threshold
Expected Frequency in Excess of a Threshold
Fits a Collective Model to a PML Curve
Fit a Collective Model to a Wishlist of References
Layer Mean of the generalized Pareto Distribution
Second Layer Moment of the Generalized Pareto Distribution
Layer Variance of the Generalized Pareto Distribution
Maximum Likelihood Estimation of the Pareto Alphas of a Generalized Pa...
Check if an object is a PGP_Model
Check if an object is a PPP_Model
Check if an object is a valid PGP_Model
Check if an object is a valid PPP_Model
Expected Loss of a Reinsurance Layer
Expected Loss of a Reinsurance Layer
Expected Loss of a Reinsurance Layer
Standard Deviation of a Reinsurance Layer
Standard Deviation of a Reinsurance Layer
Standard Deviation of a Reinsurance Layer
Variance of a Reinsurance Layer
Variance of a Reinsurance Layer
Variance of a Reinsurance Layer
Local Pareto Alpha
Distribution Function of the Pareto Distribution
Pareto Extrapolation
Pareto Alpha Between a Frequency and a Layer
Pareto Alpha Between Two Frequencies
Pareto Alpha Between Two Layers
Layer Mean of the Pareto Distribution
Second Layer Moment of the Pareto Distribution
Layer Variance of the Pareto Distribution
Maximum Likelihood Estimation of the Alpha of a Pareto distribution
Density of the Pareto Distribution
Distribution Function of the generalized Pareto Distribution
PGP_Model (Collective Panjer & Generalized Pareto Model) Object
Distribution Function of the Piecewise Pareto Distribution
Layer Mean of the Piecewise Pareto Distribution
Second Layer Moment of the Piecewise Pareto Distribution
Layer Variance of the Piecewise Pareto Distribution
Match a Tower of Expected Layers Losses
Maximum Likelihood Estimation of the Alphas of the Piecewise Pareto Di...
Density of the Piecewise Pareto Distribution
Distribution Function of the Pareto Distribution
Distribution Function of the Piecewise Pareto Distribution
PPP_Model (Collective Panjer & Piecewise Pareto Model) Object
Expected Frequency in Excess of a Threshold
Expected Loss of a Reinsurance Layer
Standard Deviation of a Reinsurance Layer
Variance of a Reinsurance Layer
Simulate Losses with a PPP_Model
Print a PGP_Model Object (Collective Panjer & Generalized Pareto Model...
Print a PPP_Model Object (Collective Panjer & Piecewise Pareto Model) ...
Quantile Function of the generalized Pareto Distribution
Quantile Function of the Pareto Distribution
Quantile Function of the Piecewise Pareto Distribution
Simulation of the generalized Pareto Distribution
Simulation of the Pareto Distribution
Simulation of the Piecewise Pareto Distribution
Simulate Losses with a PGP_Model
Simulate Losses with a PPP_Model
Simulate Losses with a Collective Model
Utilities for the Pareto, piecewise Pareto and generalized Pareto distribution that are useful for reinsurance pricing. In particular, the package provides a non-trivial algorithm that can be used to match the expected losses of a tower of reinsurance layers with a layer-independent collective risk model. The theoretical background of the matching algorithm and most other methods are described in Ulrich Riegel (2018) <doi:10.1007/s13385-018-0177-3>.